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Cost preserving bisimulations for probabilistic automata. (English) Zbl 1448.68353
Summary: Probabilistic automata constitute a versatile and elegant model for concurrent probabilistic systems. They are equipped with a compositional theory supporting abstraction, enabled by weak probabilistic bisimulation serving as the reference notion for summarising the effect of abstraction.
This paper considers probabilistic automata augmented with costs. It extends the notions of weak transitions in probabilistic automata in such a way that the costs incurred along a weak transition are captured. This gives rise to cost-preserving and cost-bounding variations of weak probabilistic bisimilarity, for which we establish compositionality properties with respect to parallel composition. Furthermore, polynomial-time decision algorithms are proposed, that can be effectively used to compute reward-bounding abstractions of Markov decision processes in a compositional manner.

MSC:
68Q85 Models and methods for concurrent and distributed computing (process algebras, bisimulation, transition nets, etc.)
68Q45 Formal languages and automata
68Q87 Probability in computer science (algorithm analysis, random structures, phase transitions, etc.)
Software:
MRMC; PRISM; SIGREF
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